Was curious what readers thought were the oddest/strangest 5th freedom flights

The fifth freedom, also referred to as beyond rights, allows an airline to carry revenue traffic between foreign countries as a part of services connecting the airline's own country.

The Havana - Managua leg below is odd

Blue Panorama to Start Managua Service from July 2012

Italian carrier Blue Panorama Airlines starting July 2012 is introducing service to Nicaragua, with one weekly service to Managua every Wednesdays. The service will begin on 11JUL12 with Boeing 767-300ER aircraft.

MIAT Mongolian (OM) operates a service from Ulaanbaatar to Berlin via Moscow (ULN-SVO-TXL), presumably their flagship international route. IIRC, it used to be operated by an A310-300 which has since been retired from the fleet, but is now flown with a 767-300ER.

This is a triangle route, which isn't how fifth freedom routes typically operate. I wouldn't be surprised if BV elected not to sell local tickets HAV-MGA given that they don't offer a return MGA-HAV option. If they do not, this actually doesn't qualify as a fifth freedom route.

With a triangle route, the idea is typically to be able to serve two distant destinations where neither necessarily has demand for a larger long-range aircraft, but where both are considered worthwhile additions to the network. The majority of the passengers to both HAV and MGA would be flying to/from FCO. The FCO-HAV leg would be carrying everyone bound for both destinations, the HAV-MGA leg would be a combination of people flying FCO-MGA or HAV-FCO, while the MGA-FCO leg then carries all of the folks bound for FCO from both cities.

As to the question of the oddest fifth freedom routes, DL 97 operating GUM-NRT-ROR seems ridiculous if not for the fact that they are really two completely unrelated sections. The non-stop distance between GUM and ROR is only 707 nm, yet DL 97 travels 3,082 nm between GUM and ROR via NRT (336% longer routing). The flight also typically changes gauge at NRT, as it usually operates as a 763 on GUM-NRT and a 752 on NRT-ROR.

Though there are likely a few connections from other US-originating flights, the NRT-ROR segment primarily exists to serve Asian demand to Palau. I imagine hardly anyone flies GUM-ROR via NRT on DL rather than taking a more direct route on UA from the GUM hub. Due to the fairly low ex-USA demand to ROR, I'm sure it makes sense for DL to connect this route to a GUM flight rather than something from the mainland given that the mainland flight numbers are continued to the major Asian destinations instead.

Quoting steex (Reply 4):This is a triangle route, which isn't how fifth freedom routes typically operate. I wouldn't be surprised if BV elected not to sell local tickets HAV-MGA given that they don't offer a return MGA-HAV option. If they do not, this actually doesn't qualify as a fifth freedom route.

I think it's actually a tech stop. FCO-MGA is really pushing the 763, especially if it's a dense (tourist) configuration.

You're likely right given that they didn't really include anything about Havana in the announcement. However, with 2 hours scheduled on the ground in HAV, it seems like they have to be doing more than just refueling. It wouldn't take that long to get a 763 ready for the hop from HAV to MGA.